(e.g., [1]}, p.141),
we can give a candidate for solution which is formally written by
\(u(t) = \int ^t_0 (t-s)^{\alpha -1}E_{\alpha ,\alpha }(-\lambda (t-s)^{\alpha }) \delta _{t_0}(s) ds,\quad 0<t<T. \qquad \mathrm {{(5.10)}}\) 
